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I am working on implementing algorithms to solve Hamiltonian Cycle Problem. I need difficult problem graphs to test my implementations but my google-fu is weak and am unable to find any.

Please advise where I might find a set of difficult graphs for the Hamiltonian Cycle, or how to generate such graphs for testing.

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TSPLIB contains some instances of Hamiltonian Cycle. Haythorpe [1] proposes a set of around a thousand instances which are claimed to be "structurally difficult" (not necessarily large).

Haythorpe, Michael. "FHCP Challenge Set: The first set of structurally difficult instances of the Hamiltonian cycle problem." arXiv preprint arXiv:1902.10352 (2019).

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